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A249919 Number of LCD (liquid-crystal display) segments needed to display n in binary.

%I A249919 #43 Jun 24 2022 19:55:17
%S A249919 6,2,8,4,14,10,10,6,20,16,16,12,16,12,12,8,26,22,22,18,22,18,18,14,22,
%T A249919 18,18,14,18,14,14,10,32,28,28,24,28,24,24,20,28,24,24,20,24,20,20,16,
%U A249919 28,24,24,20,24,20,20,16,24,20,20,16,20,16,16,12,38,34,34,30,34,30,30,26,34,30,30,26,30,26,26
%N A249919 Number of LCD (liquid-crystal display) segments needed to display n in binary.
%C A249919 The "LCD" refers to how 0 and 1 are displayed, such that zero is represented with 6 lines, and one is represented with 2 lines:
%C A249919    _
%C A249919   | |        |
%C A249919   |_|  and   |
%H A249919 Indranil Ghosh, <a href="/A249919/b249919.txt">Table of n, a(n) for n = 0..32768</a>
%F A249919 The formulas below do not include a(0)=6:
%F A249919 a(2^(n-1)) = 2 + 6(n-1).
%F A249919 a((2^n)-1) = 2n.
%F A249919 a(x) = a(2^(n+1) + (2^n)-1) = a(2^(n+2)-1) + 4.
%F A249919 a(y) = a(2^(n+1) + (2^n)) = a(2^(n+1)) - 4.
%F A249919 a(x - u) + 6 = a(x - u + 2^(n+1)).
%F A249919 a(y + u) + 6 = a(y + u + 2^(n+1)).
%F A249919 a(2^(n+1)) + a(2^(n+2)-1) = a(x - u) + a(y + u).
%F A249919 where n=1, 2, ...
%F A249919 and u=0, ..., (2^n)-2.
%F A249919 a(n) = A010371(A007088(n)). - _Michel Marcus_, Aug 01 2015
%e A249919 For n = 4, 4 = 100_2. So, a(4) = 2 + 6 + 6 = 14. - _Indranil Ghosh_, Feb 02 2017
%t A249919 f[n_] := Total[{2, 6}*(Count[ IntegerDigits[n, 2], #] & /@ {1, 0})]; Array[f, 79, 0] (* _Robert G. Wilson v_, Jul 26 2015 *)
%o A249919 (PARI)  a(n)=if(n==0, 6, 6*#binary(n) - 4*hammingweight(n)); \\ _Charles R Greathouse IV_, Feb 28 2015
%o A249919 (C)
%o A249919 // Input: n (no negative offset/term number), Output: a(n)
%o A249919 int A249919 (int n) {
%o A249919    int m=0, r=0;
%o A249919    if (n) {
%o A249919       while (n!=1) {
%o A249919          m=n&1; //equivalent to m=n%2;
%o A249919          n=n>>1; //equivalent to n/=2;
%o A249919          if (m) {
%o A249919             r+=2;
%o A249919          } else {
%o A249919             r+=6;
%o A249919          }
%o A249919       }
%o A249919       r+=2;
%o A249919    } else {
%o A249919       r+=6;
%o A249919    }
%o A249919    return r;
%o A249919 }
%o A249919 // _Arlu Genesis A. Padilla_, Jun 18 2015
%o A249919 (Python)
%o A249919 def A249919(n):
%o A249919     x=bin(n)[2:]
%o A249919     s=0
%o A249919     for i in x:
%o A249919         s+=[6,2][int(i)]
%o A249919     return s # _Indranil Ghosh_, Feb 02 2017
%Y A249919 Cf. A007088, A010371, A074458.
%K A249919 easy,nonn,base
%O A249919 0,1
%A A249919 _Arlu Genesis A. Padilla_, Jan 14 2015